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SUMMARY:Exact Results for Two-Dimensional Coarsening - Prof. Alan Bray\, U
 niversity of Manchester
DTSTART:20080221T141500Z
DTEND:20080221T154500Z
UID:TALK9778@talks.cam.ac.uk
CONTACT:Joe Bhaseen
DESCRIPTION:A system which is rapidly cooled from a  homogeneous high-temp
 erature phase into a two-phase region forms domains of the two low-tempera
 ture phases\, with a characteristic length scale that grows (the domain st
 ructure "coarsens") with time. The evolution of the domain structure is we
 ll described  by a dynamical scaling hypothesis\, according to which the d
 omain morphology is statistically time-independent apart from one overall 
 length scale (the "domain scale") that grows with time.\n\nIn this talk\, 
 exact results pertaining to the domain morphology are obtained for the cas
 e where a system described by a two-dimensional\, non-conserved scalar fie
 ld (e.g. a twisted nematic liquid crystal)\, starting from disordered init
 ial condition appropriate to the state immediately after the quench\, evol
 ves according to the curvature-driven motion of its domain walls. In parti
 cular\, the number density of  "hulls" (the outer boundaries of domains) w
 ith area A\, at time t after the quench\, is given by \n\nn(A\,t) =  2c/(A
 +lambda t)^2^\, \n\nwhere c = 1/(8 pi sqrt(3)) = 0.023 is a universal cons
 tant associated with the initial condition. This result validates (at leas
 t one aspect of) the scaling hypothesis. Exploiting the smallness of c\, a
 pproximate results are obtained for the number density of domains of area 
 A at time t. The result has\, for large t\,  the scaling form \n\nn_d(A\,t
 ) = 2 c_d (lambda_d t)^tau-2^/\n(A + lambda_d t)^tau^\, \n\nwhere c_d = c 
 + O(c^2^)\, \nlambda_d = lambda(1+ O(c^1^)) and \ntau = 187/91. The corres
 ponding results for the case where the initial state is the critical state
  will also be presented. 
LOCATION:TCM Seminar Room\, Cavendish Laboratory
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